A356044 Table read by antidiagonals: T(n,k) (n >= 3, k >= 1) is the number of regions formed in a regular n-gon by straight line segments when connecting the n corner vertices to the points dividing the sides into k equal parts.
1, 6, 4, 19, 32, 11, 30, 96, 90, 24, 61, 188, 316, 246, 50, 78, 332, 580, 672, 462, 80, 127, 460, 1081, 1476, 1590, 856, 154, 150, 712, 1510, 2442, 2982, 2688, 1476, 220, 217, 916, 2306, 3528, 5370, 5504, 4861, 2420, 375, 246, 1204, 2930, 5310, 7742, 9440, 9288, 7360, 3630, 444
Offset: 3
Examples
The table begins: 1, 6, 19, 30, 61, 78, 127, 150, 217, 246,... 4, 32, 96, 188, 332, 460, 712, 916, 1204, 1488,... 11, 90, 316, 580, 1081, 1510, 2306, 2930, 3961, 4780,... 24, 246, 672, 1476, 2442, 3528, 5310, 7176, 9072, 11352,... 50, 462, 1590, 2982, 5370, 7742, 11390, 14742, 19650, 23982,... 80, 856, 2688, 5504, 9440, 13968, 20216, 27008, 34888, 43792,... 154, 1476, 4861, 9288, 16408, 23886, 34741, 45324, 59860, 73548,... 220, 2420, 7360, 14980, 25480, 37690, 54180, 72280, 93400, 116970,... 375, 3630, 11661, 22374, 39051, 57222, 82545, 108174, 142143, 175230,... 444, 5400, 15864, 32532, 55500, 82032, 118056, 157236, 203148, 254184,... 781, 7566, 23804, 45890, 79431, 116818, 167662, 220350, 288497, 356486,... 952, 10668, 31682, 63700, 107184, 160874, 226996, 303324, 390950, 489860,... 1456, 14070, 43546, 84270, 144976, 213720, 305656, 402510, 525586, 650550,... 1696, 18832, 55792, 111840, 187776, 282000, 397072, 530432, 683616, 855920,... 2500, 24072, 73645, 142732, 244410, 361012, 514795, 678912, 884800, 1096432,... 2466, 30078, 91080, 181746, 306522, 458334, 647766, 864234, 1114668, 1394586,... 4029, 38646, 117079, 227278, 387753, 573534, 816051, 1077414, 1401973, 1738918,... . . See the attached text file for more examples and the cross references for further images.
Links
- Scott R. Shannon, Image of T(5,9) = 3961.
- Scott R. Shannon, Image of T(6,8) = 7176.
- Scott R. Shannon, Image of T(7,5) = 5370.
- Scott R. Shannon, Image of T(8,4) = 5504.
- Scott R. Shannon, Image of T(12,4) = 32532.
- Scott R. Shannon, Image of T(14,6) = 160874.
- Scott R. Shannon, Table for n = 3..25.
